6.88 Problems 8701 to 8800

Table 6.175: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

8701

\[ {} y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime } = 0 \]

8702

\[ {} \left (1+y^{2}\right ) \left ({\mathrm e}^{2 x}-{\mathrm e}^{y} y^{\prime }\right )-\left (1+y\right ) y^{\prime } = 0 \]

8703

\[ {} \left (x +y\right ) y^{\prime }+x -y = 0 \]

8704

\[ {} y-2 x y+x^{2} y^{\prime } = 0 \]

8705

\[ {} 2 x y^{\prime } = \left (2 x^{2}-y^{2}\right ) y \]

8706

\[ {} x^{2} y^{\prime }+y^{2} = y y^{\prime } x \]

8707

\[ {} \left (x^{2}+y^{2}\right ) y^{\prime } = 2 x y \]

8708

\[ {} x y^{\prime }-y = x \tan \left (\frac {y}{x}\right ) \]

8709

\[ {} x y^{\prime } = y-{\mathrm e}^{\frac {y}{x}} x \]

8710

\[ {} x y^{\prime }-y = \left (x +y\right ) \ln \left (\frac {x +y}{x}\right ) \]

8711

\[ {} x y^{\prime } = y \cos \left (\frac {y}{x}\right ) \]

8712

\[ {} y+\sqrt {x y}-x y^{\prime } = 0 \]

8713

\[ {} x y^{\prime }-\sqrt {x^{2}-y^{2}}-y = 0 \]

8714

\[ {} x +y-\left (x -y\right ) y^{\prime } = 0 \]

8715

\[ {} x^{2}+2 x y-y^{2}+\left (y^{2}+2 x y-x^{2}\right ) y^{\prime } = 0 \]

8716

\[ {} x y^{\prime }-y = y y^{\prime } \]

8717

\[ {} y^{2}+\left (x^{2}-x y\right ) y^{\prime } = 0 \]

8718

\[ {} x^{2}+x y+y^{2} = x^{2} y^{\prime } \]

8719

\[ {} \frac {1}{x^{2}-x y+y^{2}} = \frac {y^{\prime }}{2 y^{2}-x y} \]

8720

\[ {} y^{\prime } = \frac {2 x y}{3 x^{2}-y^{2}} \]

8721

\[ {} y^{\prime } = \frac {x}{y}+\frac {y}{x} \]

8722

\[ {} x y^{\prime } = y+\sqrt {-x^{2}+y^{2}} \]

8723

\[ {} \left (2 \sqrt {x y}-x \right ) y^{\prime }+y = 0 \]

8724

\[ {} x y^{\prime } = y \ln \left (\frac {y}{x}\right ) \]

8725

\[ {} y^{\prime } \left (y^{\prime }+y\right ) = x \left (x +y\right ) \]

8726

\[ {} \left (x y^{\prime }+y\right )^{2} = y^{2} y^{\prime } \]

8727

\[ {} x^{2} {y^{\prime }}^{2}-3 y y^{\prime } x +2 y^{2} = 0 \]

8728

\[ {} x y^{\prime }-y = \sqrt {x^{2}+y^{2}} \]

8729

\[ {} y {y^{\prime }}^{2}+2 x y^{\prime }-y = 0 \]

8730

\[ {} y^{\prime }+\frac {2 y+x}{x} = 0 \]

8731

\[ {} y^{\prime } = \frac {y}{x +y} \]

8732

\[ {} x y^{\prime } = x +\frac {y}{2} \]

8733

\[ {} y^{\prime } = \frac {x +y-2}{y-x -4} \]

8734

\[ {} 2 x -4 y+6+\left (x +y-2\right ) y^{\prime } = 0 \]

8735

\[ {} y^{\prime } = \frac {2 y-x +5}{2 x -y-4} \]

8736

\[ {} y^{\prime } = -\frac {4 x +3 y+15}{2 x +y+7} \]

8737

\[ {} y^{\prime } = \frac {x +3 y-5}{x -y-1} \]

8738

\[ {} y^{\prime } = \frac {2 \left (y+2\right )^{2}}{\left (x +y+1\right )^{2}} \]

8739

\[ {} 2 x +y+1-\left (4 x +2 y-3\right ) y^{\prime } = 0 \]

8740

\[ {} x -y-1+\left (y-x +2\right ) y^{\prime } = 0 \]

8741

\[ {} \left (x +4 y\right ) y^{\prime } = 2 x +3 y-5 \]

8742

\[ {} y+2 = \left (2 x +y-4\right ) y^{\prime } \]

8743

\[ {} \left (1+y^{\prime }\right ) \ln \left (\frac {x +y}{x +3}\right ) = \frac {x +y}{x +3} \]

8744

\[ {} y^{\prime } = \frac {x -2 y+5}{y-2 x -4} \]

8745

\[ {} y^{\prime } = \frac {3 x -y+1}{2 x +y+4} \]

8746

\[ {} 2 x y^{\prime }+\left (x^{2} y^{4}+1\right ) y = 0 \]

8747

\[ {} 2 x \left (x -y^{2}\right ) y^{\prime }+y^{3} = 0 \]

8748

\[ {} x^{3} \left (y^{\prime }-x \right ) = y^{2} \]

8749

\[ {} 2 x^{2} y^{\prime } = y^{3}+x y \]

8750

\[ {} y+x \left (2 x y+1\right ) y^{\prime } = 0 \]

8751

\[ {} 2 y^{\prime }+x = 4 \sqrt {y} \]

8752

\[ {} y^{\prime } = y^{2}-\frac {2}{x^{2}} \]

8753

\[ {} 2 x y^{\prime }+y = y^{2} \sqrt {x -x^{2} y^{2}} \]

8754

\[ {} \frac {2 y y^{\prime } x}{3} = \sqrt {x^{6}-y^{4}}+y^{2} \]

8755

\[ {} 2 y+\left (x^{2} y+1\right ) x y^{\prime } = 0 \]

8756

\[ {} x \left (1-x y\right ) y^{\prime }+\left (x y+1\right ) y = 0 \]

8757

\[ {} \left (1+x^{2} y^{2}\right ) y+\left (x^{2} y^{2}-1\right ) x y^{\prime } = 0 \]

8758

\[ {} \left (x^{2}-y^{4}\right ) y^{\prime }-x y = 0 \]

8759

\[ {} y \left (1+\sqrt {x^{2} y^{4}-1}\right )+2 x y^{\prime } = 0 \]

8760

\[ {} x \left (2-9 x y^{2}\right )+y \left (4 y^{2}-6 x^{3}\right ) y^{\prime } = 0 \]

8761

\[ {} \frac {y}{x}+\left (y^{3}+\ln \left (x \right )\right ) y^{\prime } = 0 \]

8762

\[ {} 3+2 x +\left (-2+2 y\right ) y^{\prime } = 0 \]

8763

\[ {} 2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0 \]

8764

\[ {} y^{\prime \prime }+2 y^{\prime }-y = 0 \]

8765

\[ {} y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = 0 \]

8766

\[ {} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+y = 0 \]

8767

\[ {} y^{\prime \prime }-\cot \left (x \right ) y^{\prime }+y \cos \left (x \right ) = 0 \]

8768

\[ {} y^{\prime \prime }+\frac {y^{\prime }}{x}+x^{2} y = 0 \]

8769

\[ {} x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-x^{2}+1\right ) y^{\prime }-2 y = 0 \]

8770

\[ {} y-x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0 \]

8771

\[ {} y^{\prime \prime \prime }-2 x y^{\prime \prime }+4 x^{2} y^{\prime }+8 x^{3} y = 0 \]

8772

\[ {} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+y \,{\mathrm e}^{x} = 0 \]

8773

\[ {} x^{2} y^{\prime \prime }+2 x y^{\prime }+4 y = 0 \]

8774

\[ {} x^{4} y^{\prime \prime \prime \prime }-x^{2} y^{\prime \prime }+y = 0 \]

8775

\[ {} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+y = 0 \]

8776

\[ {} y+x y^{\prime }+y^{\prime \prime } = 2 x \,{\mathrm e}^{x}-1 \]

8777

\[ {} x y^{\prime \prime }+x y^{\prime }-y = x^{2}+2 x \]

8778

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{2}+2 x \]

8779

\[ {} -y+x y^{\prime }+x^{3} y^{\prime \prime } = \cos \left (\frac {1}{x}\right ) \]

8780

\[ {} x \left (1+x \right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }-y = x +\frac {1}{x} \]

8781

\[ {} 2 x y^{\prime \prime }+\left (x -2\right ) y^{\prime }-y = x^{2}-1 \]

8782

\[ {} x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (4 x +3\right ) y^{\prime }-y = x +\frac {1}{x} \]

8783

\[ {} x^{2} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-x y^{\prime }+y = x \left (1-\ln \left (x \right )\right )^{2} \]

8784

\[ {} x y^{\prime \prime }+2 y^{\prime }+x y = \sec \left (x \right ) \]

8785

\[ {} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\frac {y}{4} = -\frac {x^{2}}{2}+\frac {1}{2} \]

8786

\[ {} \left (\cos \left (x \right )+\sin \left (x \right )\right ) y^{\prime \prime }-2 \cos \left (x \right ) y^{\prime }+\left (\cos \left (x \right )-\sin \left (x \right )\right ) y = \left (\cos \left (x \right )+\sin \left (x \right )\right )^{2} {\mathrm e}^{2 x} \]

8787

\[ {} \left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime \prime }-2 y^{\prime } \sin \left (x \right )+y \left (\cos \left (x \right )+\sin \left (x \right )\right ) = \left (\cos \left (x \right )-\sin \left (x \right )\right )^{2} \]

8788

\[ {} y^{\prime } = x^{2} \left (1+y^{2}\right ) \]

8789

\[ {} y^{\prime } = \frac {x^{2}}{1-y^{2}} \]

8790

\[ {} y^{\prime } = \frac {3 x^{2}+4 x +2}{-2+2 y} \]

8791

\[ {} x y^{\prime }-2 \sqrt {x y} = y \]

8792

\[ {} y^{\prime } = \frac {x +y-1}{x -y+3} \]

8793

\[ {} {\mathrm e}^{x}+y+\left (x -2 \sin \left (y\right )\right ) y^{\prime } = 0 \]

8794

\[ {} 3 x +\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime } = 0 \]

8795

\[ {} x^{2} y^{\prime }+y^{2}-x y = 0 \]

8796

\[ {} x +y-\left (x -y\right ) y^{\prime } = 0 \]

8797

\[ {} y^{\prime } = \frac {y}{2 x}+\frac {x^{2}}{2 y} \]

8798

\[ {} y^{\prime } = -\frac {2}{t}+\frac {y}{t}+\frac {y^{2}}{t} \]

8799

\[ {} y^{\prime } = -\frac {y}{t}-1-y^{2} \]

8800

\[ {} y y^{\prime }+x = a {y^{\prime }}^{2} \]